Moments for stationary Markov chains with asymptotically zero drift

被引：0

作者：

Korshunov D.A. ^{[1
]}

机构：

[1] Sobolev Institute of Mathematics, Novosibirsk

来源：

Siberian Mathematical Journal | 2011年 / 52卷 / 4期

基金：

俄罗斯基础研究基金会;

关键词：

asymptotically zero drift; equilibrium identity; heavy-tailed distribution; invariant distribution; power moments; stationary Markov chain; test (Lyapunov) functions; Weibull-type moments;

D O I：

10.1134/S0037446611040100

中图分类号：

学科分类号：

摘要：

We consider a Markov chain on ℝ+ with asymptotically zero drift and finite second moments of jumps. We assume that the chain has invariant distribution. The paper is devoted to the existence and nonexistence of moments of invariant distribution. Our analysis is based on the technique of test functions. © 2011 Pleiades Publishing, Ltd.

引用

页码：655 / 664

页数：9

共 12 条

[1]

Kiefer J., Wolfowitz J., On the characteristics of the general queueing process with applications to random walk, Ann. Math. Statist., 27, pp. 147-161, (1956)

[2]

Lamperti J., Criteria for the recurrence or transience of stochastic processes. I, J. Math. Anal. Appl., 1, 3-4, pp. 314-330, (1960)

[3]

Mein S., Tweedie R.L., Markov Chains and Stochastic Stability, (1993)

[4]

Menshikov M.V., Popov S.Y., Exact power estimates for countable Markov chains, Markov Process. Related Fields, 1, 1, pp. 57-78, (1995)

[5]

Korshunov D., Transition phenomena for real-valued Markov chains, Siberian Adv. Math., 3, 4, pp. 53-100, (1993)

[6]

Baccelli F., Bremaud P., Elements of Queueing Theory, (1994)

[7]

Foss S.G., Chernova N.I., Dominance theorems and ergodic properties of polling systems, Problems Inform. Transmission, 32, 4, pp. 342-364, (1996)

[8]

Nazarov L.V., Smirnov S.N., Estimation of moments of a stationary distribution of a Markov chain by the method of test functions, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., 4, pp. 43-48, (1985)

[9]

Tweedie R.L., The existence of moments for stationary Markov chains, J. Appl. Probab., 20, 1, pp. 191-196, (1983)

[10]

Menshikov M.V., Asymont I.M., Yasnogorodskij R., Markov processes with asymptotically zero drifts, Problems Inform. Transmission, 31, 3, pp. 248-261, (1995)

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